Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Problem 6.5 OPTIONAL PROBLEM - Homogeneous functions A function f(x, y, z) is called homogeneous of degree > if f(bx, by, bz) = b^f(x, y, z) for b, A E R. Such functions are also called scale free. Prove Euler's theorem for homogeneous functions which states that if f(x, y, z) is homogeneous of degree X, then af af af x +y +z = əx dy Əz Xf. Hint: Define intermediate variables u = bx, v= by and w bz. Then, differentiate the given equation f(bx, by, bz) = bf(x, y, z) with respect to x, y, z and b, using the chain rule.
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Transcribed Image Text:Problem 6.5 OPTIONAL PROBLEM - Homogeneous functions A function f(x, y, z) is called homogeneous of degree > if f(bx, by, bz) = b^f(x, y, z) for b, A E R. Such functions are also called scale free. Prove Euler's theorem for homogeneous functions which states that if f(x, y, z) is homogeneous of degree X, then af af af x +y +z = əx dy Əz Xf. Hint: Define intermediate variables u = bx, v= by and w bz. Then, differentiate the given equation f(bx, by, bz) = bf(x, y, z) with respect to x, y, z and b, using the chain rule.
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